# Classroom Voting Questions Multivariable Calculus

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```							             Classroom Voting Questions:
Multivariable Calculus

15.2 Optimization

1. Estimate the global maximum and minimum of the functions whose level curves are
given below. How many times does each occur?

(a) Max ≈ 6, occurring once; min ≈ −6, occurring once
(b) Max ≈ 6, occurring once; min ≈ −6, occurring twice
(c) Max ≈ 6, occurring twice; min ≈ −6, occurring twice
(d) Max ≈ 6, occurring three times; min ≈ −6, occurring three times
(e) None of the above

2. What are the global maximum and minimum values of f (x, y) = x2 + y 2 on the
triangular region in the ﬁrst quadrant bounded by x + y = 2, x = 0, y = 0?

(a) Maximum = 2, Minimum = -2
(b) Maximum = 2, Minimum = 0

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(c) Maximum = 4, Minimum = 2
(d) Maximum = 4, Minimum = 0

3. The function f (x, y) = x3 + 12xy + y 4 has:

(a) no global maxes or mins
(b) a global max, but no global min
(c) a global min, but no global max
(d) both a global min and a global max

4. Which of the following would be enough evidence to conclude that a smooth function
f (x, y) has a global min?

(a) D is always positive
(b) fxx > 0 and fyy > 0
(c) f (x, y) has no saddle points or local maxes
(d) none of the above

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```
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